From 52230cc17788a02f8c79b345119508062e1ab036 Mon Sep 17 00:00:00 2001 From: aarne Date: Fri, 8 Jun 2007 09:59:06 +0000 Subject: [PATCH] overloaded Swedish paradigms --- lib/resource-1.0/swedish/IrregSwe.gf | 2 +- lib/resource-1.0/swedish/ParadigmsSwe.gf | 350 ++++++++++++++--------- 2 files changed, 221 insertions(+), 131 deletions(-) diff --git a/lib/resource-1.0/swedish/IrregSwe.gf b/lib/resource-1.0/swedish/IrregSwe.gf index 25f63a0fa..a31fd7241 100644 --- a/lib/resource-1.0/swedish/IrregSwe.gf +++ b/lib/resource-1.0/swedish/IrregSwe.gf @@ -177,7 +177,7 @@ concrete IrregSwe of IrregSweAbs = CatSwe ** open ParadigmsSwe in { utbrista_V = irregV "utbrista" "utbrast" "utbrustit" ; utesluta_V = irregV "utesluta" "uteslöt" "uteslutit" ; utskriva_V = irregV "utskriva" "utskrev" "utskrivit" ; - veta_V = mkV "veta" "vet" "vet" "visste" "vetat" (variants {}) ; + veta_V = mk6V "veta" "vet" "vet" "visste" "vetat" (variants {}) ; vända_V = irregV "vända" "vände" "vänt" ; vina_V = irregV "vina" "ven" "vinit" ; vinna_V = irregV "vinna" "vann" "vunnit" ; diff --git a/lib/resource-1.0/swedish/ParadigmsSwe.gf b/lib/resource-1.0/swedish/ParadigmsSwe.gf index d1564a4f0..93ea0d390 100644 --- a/lib/resource-1.0/swedish/ParadigmsSwe.gf +++ b/lib/resource-1.0/swedish/ParadigmsSwe.gf @@ -58,60 +58,53 @@ oper nominative : Case ; genitive : Case ; --- Prepositions used in many-argument functions are just strings. +-- Prepositions used in many-argument functions can be constructed from strings. mkPrep : Str -> Prep ; noPrep : Prep ; -- empty string + --2 Nouns --- Worst case: give all four forms. The gender is computed from the --- last letter of the second form (if "n", then $utrum$, otherwise $neutrum$). +-- The following overloaded paradigm takes care of all noun formation. - mkN : (apa,apan,apor,aporna : Str) -> N ; + mkN : overload { + mkN : (apa : Str) -> N ; + mkN : (lik : Str) -> Gender -> N ; + mkN : (nyckel,nycklar : Str) -> N ; + mkN : (museum,museet,museer,museerna : Str) -> N + } ; --- The regular function takes the singular indefinite form and computes the other --- forms and the gender by a heuristic. The heuristic is currently --- to treat all words ending with "a" like "flicka", with "e" like "rike", --- and otherwise like "bil". --- If in doubt, use the $cc$ command to test! +-- The one-argument case takes the singular indefinite form and computes +-- the other forms and the gender by a simple heuristic. The heuristic is currently +-- to treat all words ending with "a" like "apa-apor", with "e" like "rike-riken", +-- and otherwise like "bil-bilar". - regN : Str -> N ; +-- The case with a string and gender makes it possible to treat +-- "lik" (neutrum) and "pojke" (utrum). --- Adding the gender manually greatly improves the correction of $regN$. +-- Giving two forms - the singular and plural indefinite - is sufficient for +-- most nouns. The paradigm deals correctly with the vowel contractions in +-- "nyckel - nycklar" such as "pojke - pojkar". - regGenN : Str -> Gender -> N ; +-- In the worst case, four forms are needed. --- In practice the worst case is often just: give singular and plural indefinite. - - mk2N : (nyckel,nycklar : Str) -> N ; - --- This heuristic takes just the plural definite form and infers the others. --- It does not work if there are changes in the stem. - - mk1N : (bilarna : Str) -> N ; - - ---3 Compound nouns --- --- All the functions above work quite as well to form compound nouns, +-- All the functions above work quite as well to form **compound nouns**, -- such as "fotboll". + --3 Relational nouns -- --- Relational nouns ("dotter till x") need a preposition. +-- Relational nouns ("kung av x") are nouns with a preposition. +-- As a special case, we provide regular nouns (formed with one-argument $mkN$) +-- with the preposition "av". - mkN2 : N -> Prep -> N2 ; + mkN2 : overload { + mkN2 : Str -> N2 ; + mkN2 : N -> Prep -> N2 + } ; --- The most common preposition is "av", and the following is a --- shortcut for regular, $nonhuman$ relational nouns with "av". - - regN2 : Str -> Gender -> N2 ; - --- Use the function $mkPreposition$ or see the section on prepositions below to --- form other prepositions. --- -- Three-place relational nouns ("förbindelse från x till y") -- need two prepositions. @@ -128,39 +121,28 @@ oper -- --3 Proper names and noun phrases -- --- Proper names, with a regular genitive, are formed as follows +-- Proper names, with a regular genitive, are formed from strings and +-- have the default gender utrum. In the worst case, the genitive form +-- is irregular. - regGenPN : Str -> Gender -> PN ; - regPN : Str -> PN ; -- utrum + mkPN : overload { + mkPN : Str -> PN ; + mkPN : Str -> Gender -> PN ; + mkPN : (jesus,jesu : Str) -> Gender -> PN + } ; --- Sometimes you can reuse a common noun as a proper name, e.g. "Bank". - - nounPN : N -> PN ; - --- To form a noun phrase that can also be plural and have an irregular --- genitive, you can use the worst-case function. - - mkNP : Str -> Str -> Number -> Gender -> NP ; --2 Adjectives --- Adjectives may need as many as seven forms. +-- Adjectives need one to seven forms. - mkA : (liten, litet, lilla, sma, mindre, minst, minsta : Str) -> A ; - --- The regular pattern works for many adjectives, e.g. those ending --- with "ig". - - regA : Str -> A ; - --- Just the comparison forms can be irregular. - - irregA : (tung,tyngre,tyngst : Str) -> A ; - --- Sometimes just the positive forms are irregular. - - mk3A : (galen,galet,galna : Str) -> A ; - mk2A : (bred,brett : Str) -> A ; + mkA : overload { + mkA : (billig : Str) -> A ; + mkA : (bred,brett : Str) -> A ; -- also galen-galet(-galna) + mkA : (tung,tyngre,tyngst : Str) -> A ; + mkA : (god,gott,goda,battre,bast : Str) -> A ; + mkA : (liten,litet,lilla,sma,mindre,minst,minsta : Str) -> A + } ; -- Comparison forms may be compound ("mera svensk" - "mest svensk"). @@ -189,36 +171,33 @@ oper --2 Verbs -- --- The worst case needs five forms. +-- All verbs can be defined by the overloaded paradigm $mkV$. - mkV : (supa,super,sup,söp,supit,supen : Str) -> V ; + mkV : overload { + mkV : (stämmer : Str) -> V ; + mkV : (dricka,drack,druckit : Str) -> V ; + mkV : (gå,går,gå,gick,gått,gången : Str) -> V ; + mkV : V -> Str -> V + } ; --- The 'regular verb' function is inspired by Lexin. It uses the +-- The 'regular verb' (= one-place) case is inspired by Lexin. It uses the -- present tense indicative form. The value is the first conjugation if the -- argument ends with "ar" ("tala" - "talar" - "talade" - "talat"), -- the second with "er" ("leka" - "leker" - "lekte" - "lekt", with the --- variations like "gräva", "vända", "tyda", "hyra"), and +-- variations like in "gräva", "vända", "tyda", "hyra"), and -- the third in other cases ("bo" - "bor" - "bodde" - "bott"). +-- It is also possible to give the infinite form to it; they are treated +-- as if they were implicitly suffixed by "r". Moreover, deponent verbs +-- are recognized from the final "s". - regV : (talar : Str) -> V ; +-- Most irregular verbs need just the conventional three forms. --- The almost regular verb function needs the infinitive and the preteritum. --- It is not really more powerful than the new implementation of --- $regV$ based on the indicative form. +-- In the worst case, six forms are given. - mk2V : (leka,lekte : Str) -> V ; - --- There is an extensive list of irregular verbs in the module $IrregSwe$. --- In practice, it is enough to give three forms, as in school books. - - irregV : (dricka, drack, druckit : Str) -> V ; +-- The last case of $mkV$ is for particle verbs, such as "passa på". ---3 Verbs with a particle. --- --- The particle, such as in "passa på", is given as a string. - partV : V -> Str -> V ; --3 Deponent verbs. -- @@ -230,21 +209,30 @@ oper --3 Two-place verbs -- --- Two-place verbs need a preposition, except the special case with direct object. --- (transitive verbs). Notice that a particle comes from the $V$. +-- Two-place verbs need a preposition, which default to the 'empty preposition' +-- i.e. direct object. (transitive verbs). The simplest case is a regular +-- verb (as in $mkV$) with a direct object. +-- Notice that, if a particle is needed, it comes from the $V$. - mkV2 : V -> Prep -> V2 ; + mkV2 : overload { + mkV2 : Str -> V2 ; + mkV2 : V -> V2 ; + mkV2 : V -> Prep -> V2 + } ; - dirV2 : V -> V2 ; --3 Three-place verbs -- -- Three-place (ditransitive) verbs need two prepositions, of which --- the first one or both can be absent. +-- the first one or both can be absent. The simplest case is a regular +-- verb (as in $mkV$) with no prepositions. - mkV3 : V -> Prep -> Prep -> V3 ; -- tala, med, om - dirV3 : V -> Prep -> V3 ; -- ge, (acc),till - dirdirV3 : V -> V3 ; -- ge, (dat), (acc) + mkV3 : overload { + mkV3 : Str -> V3 ; + mkV3 : V -> V3 ; + mkV3 : V -> Prep -> V3 ; + mkV3 : V -> Prep -> Prep -> V3 + } ; --3 Other complement patterns -- @@ -293,7 +281,14 @@ oper mkPrep p = {s = p ; lock_Prep = <>} ; noPrep = mkPrep [] ; - mkN = \apa,apan,apor,aporna -> { + mkN = overload { + mkN : (apa : Str) -> N = regN ; + mkN : Str -> Gender -> N = regGenN ; + mkN : (nyckel, nycklar : Str) -> N = mk2N ; + mkN : (museum,museet,museer,museerna : Str) -> N = mk4N + } ; + + mk4N : (museum,museet,museer,museerna : Str) -> N = \apa,apan,apor,aporna -> { s = nounForms apa apan apor aporna ; g = case last apan of { "n" => Utr ; @@ -301,14 +296,14 @@ oper } } ** {lock_N = <>} ; - regN bil = regGenN bil g where { + regN : Str -> N = \bil -> regGenN bil g where { g = case of { _ + "e" => Neutr ; _ => Utr } } ; - regGenN bil g = case g of { + regGenN : Str -> Gender -> N = \bil, g -> case g of { Utr => case last bil of { "a" => decl1Noun bil ; _ => decl2Noun bil @@ -319,7 +314,7 @@ oper } } ** {lock_N = <>} ; - mk1N bilarna = case bilarna of { + mk1N : Str -> N = \bilarna -> case bilarna of { ap + "orna" => decl1Noun (ap + "a") ; bil + "arna" => decl2Noun bil ; rad + "erna" => decl3Noun rad ; @@ -327,28 +322,28 @@ oper husen => decl5Noun (Predef.tk 2 husen) } ; - mk2N bil bilar = + mk2N : Str -> Str -> N = \bil,bilar -> ifTok N bil bilar (decl5Noun bil) ( case Predef.dp 2 bilar of { "or" => case bil of { _ + "a" => decl1Noun bil ; -- apa, apor - _ + "o" => mkN bil (bil + "n") bilar (bilar + "na") ; -- ko,kor - _ => mkN bil (bil + "en") bilar (bilar + "na") -- ros,rosor + _ + "o" => mk4N bil (bil + "n") bilar (bilar + "na") ; -- ko,kor + _ => mk4N bil (bil + "en") bilar (bilar + "na") -- ros,rosor } ; "ar" => decl2Noun bil ; "er" => case bil of { - _ + "or" => mkN bil (bil + "n") bilar (bilar + "na") ; -- motor,motorn + _ + "or" => mk4N bil (bil + "n") bilar (bilar + "na") ; -- motor,motorn _ => decl3gNoun bil bilar -- fot, fötter } ; "en" => decl4Noun bil ; -- rike, riken - _ => mkN bil (bil + "et") bilar (bilar + "n") -- centrum, centra + _ => mk4N bil (bil + "et") bilar (bilar + "n") -- centrum, centra }) ; -- School declensions. decl1Noun : Str -> N = \apa -> let ap = init apa in - mkN apa (apa + "n") (ap + "or") (ap + "orna") ; + mk4N apa (apa + "n") (ap + "or") (ap + "orna") ; decl2Noun : Str -> N = \bil -> let @@ -360,35 +355,50 @@ oper sock + "e" + "n" => ; _ => } ; - in mkN bil bb.p2 bb.p1 (bb.p1 + "na") ; + in mk4N bil bb.p2 bb.p1 (bb.p1 + "na") ; decl3Noun : Str -> N = \sak -> case last sak of { - "e" => mkN sak (sak + "n") (sak +"r") (sak + "rna") ; - "y" | "å" | "é" | "y" => mkN sak (sak + "n") (sak +"er") (sak + "erna") ; - _ => mkN sak (sak + "en") (sak + "er") (sak + "erna") + "e" => mk4N sak (sak + "n") (sak +"r") (sak + "rna") ; + "y" | "å" | "é" | "y" => mk4N sak (sak + "n") (sak +"er") (sak + "erna") ; + _ => mk4N sak (sak + "en") (sak + "er") (sak + "erna") } ; decl3gNoun : Str -> Str -> N = \sak,saker -> case last sak of { - "e" => mkN sak (sak + "n") saker (saker + "na") ; - "y" | "å" | "é" | "y" => mkN sak (sak + "n") saker (saker + "na") ; - _ => mkN sak (sak + "en") saker (saker + "na") + "e" => mk4N sak (sak + "n") saker (saker + "na") ; + "y" | "å" | "é" | "y" => mk4N sak (sak + "n") saker (saker + "na") ; + _ => mk4N sak (sak + "en") saker (saker + "na") } ; decl4Noun : Str -> N = \rike -> - mkN rike (rike + "t") (rike + "n") (rike + "na") ; + mk4N rike (rike + "t") (rike + "n") (rike + "na") ; decl5Noun : Str -> N = \lik -> case Predef.dp 3 lik of { - "are" => mkN lik (lik + "n") lik (init lik + "na") ; -- kikare - _ => mkN lik (lik + "et") lik (lik + "en") + "are" => mk4N lik (lik + "n") lik (init lik + "na") ; -- kikare + _ => mk4N lik (lik + "et") lik (lik + "en") } ; + mkN2 = overload { + mkN2 : Str -> N2 = \s -> mmkN2 (regN s) (mkPrep "av") ; + mkN2 : N -> Prep -> N2 = mmkN2 + } ; - mkN2 = \n,p -> n ** {lock_N2 = <> ; c2 = p.s} ; - regN2 n g = mkN2 (regGenN n g) (mkPrep "av") ; + mmkN2 : N -> Prep -> N2 ; + regN2 : Str -> Gender -> N2 ; + + + mmkN2 = \n,p -> n ** {lock_N2 = <> ; c2 = p.s} ; + regN2 n g = mmkN2 (regGenN n g) (mkPrep "av") ; mkN3 = \n,p,q -> n ** {lock_N3 = <> ; c2 = p.s ; c3 = q.s} ; + mkPN = overload { + mkPN : Str -> PN = regPN ; + mkPN : Str -> Gender -> PN = regGenPN ; + mkPN : (jesus,jesu : Str) -> Gender -> PN = \jesus,jesu,g -> + {s = table {Nom => jesus ; Gen => jesu} ; g = g ; lock_PN = <>} ; + } ; + regPN n = regGenPN n utrum ; regGenPN n g = {s = \\c => mkCase c n ; g = g} ** {lock_PN = <>} ; nounPN n = {s = n.s ! singular ! Indef ; g = n.g ; lock_PN = <>} ; @@ -396,7 +406,23 @@ oper {s = table {NPPoss _ => y ; _ => x} ; a = agrP3 g n ; p = P3 ; lock_NP = <>} ; - mkA a b c d e f g = mkAdjective a b c d e f g ** {isComp = False ; lock_A = <>} ; + mkA = overload { + mkA : (billig : Str) -> A = regA ; + mkA : (bred,brett : Str) -> A = mk2A ; + mkA : (tung,tyngre,tyngst : Str) -> A = irregA ; + mkA : (god,gott,goda,battre,bast : Str) -> A = + \liten,litet,lilla,mindre,minst -> + mk7A liten litet lilla lilla mindre minst (minst + "a") ; + mkA : (liten,litet,lilla,sma,mindre,minst,minsta : Str) -> A = mk7A + } ; + + + regA : Str -> A ; + mk2A : (bred,brett : Str) -> A ; + irregA : (tung,tyngre,tyngst : Str) -> A ; + mk7A : (liten,litet,lilla,sma,mindre,minst,minsta : Str) -> A ; + + mk7A a b c d e f g = mkAdjective a b c d e f g ** {isComp = False ; lock_A = <>} ; regA fin = let fint : Str = case fin of { ru + "nd" => ru + "nt" ; @@ -408,13 +434,16 @@ oper in mk3A fin fint (fin + "a") ; irregA ung yngre yngst = - mkA ung (ung + "t") (ung + "a") (ung + "a") yngre yngst (yngst+"a") ; + mk7A ung (ung + "t") (ung + "a") (ung + "a") yngre yngst (yngst+"a") ; mk3A ljummen ljummet ljumma = - mkA + mk7A ljummen ljummet ljumma ljumma (ljumma + "re") (ljumma + "st") (ljumma + "ste") ; - mk2A vid vitt = mk3A vid vitt (vid + "a") ; + mk2A vid vitt = case of { + => mk3A vid vitt (gal + "na") ; + _ => mk3A vid vitt (vid + "a") + } ; compoundA adj = {s = adj.s ; isComp = True ; lock_A = <>} ; @@ -424,7 +453,14 @@ oper mkAdV x = ss x ** {lock_AdV = <>} ; mkAdA x = ss x ** {lock_AdA = <>} ; - mkV = \finna,finner,finn,fann,funnit,funnen -> + mkV = overload { + mkV : (stämmer : Str) -> V = regV ; + mkV : (dricka,drack,druckit : Str) -> V = irregV ; + mkV : (supa,super,sup,söp,supit,supen : Str) -> V = mk6V ; + mkV : V -> Str -> V = partV + } ; + + mk6V = \finna,finner,finn,fann,funnit,funnen -> let funn = ptPretForms funnen ; funnet = funn ! Strong SgNeutr ! Nom ; @@ -438,6 +474,9 @@ oper lek + "ar" => conj1 (lek + "a") ; lek + "er" => conj2 (lek + "a") ; bo + "r" => conj3 bo ; + ret + "as" => depV (conj1 (ret + "a")) ; + n + ("os" | "ys" | "ås" | "ös") => depV (conj3 (init leker)) ; + ret + "s" => depV (conj2 (ret + "a")) ; _ => conj3 leker } ; @@ -450,7 +489,7 @@ oper -- school conjugations conj1 : Str -> V = \tala -> - mkV tala (tala + "r") tala (tala +"de") (tala +"t") (tala +"d") ; + mk6V tala (tala + "r") tala (tala +"de") (tala +"t") (tala +"d") ; conj2 : Str -> V = \leka -> let lek = init leka in @@ -460,19 +499,19 @@ oper _ + "mm" => init lek ; _ => lek } - in mkV leka (lek + "er") gom (gom +"de") (gom +"t") (gom +"d") ; + in mk6V leka (lek + "er") gom (gom +"de") (gom +"t") (gom +"d") ; "r" => - mkV leka lek lek (lek +"de") (lek +"t") (lek +"d") ; + mk6V leka lek lek (lek +"de") (lek +"t") (lek +"d") ; _ => case leka of { _ + "nd" => - mkV leka (lek + "er") lek (lek +"e") (init lek +"t") lek ; + mk6V leka (lek + "er") lek (lek +"e") (init lek +"t") lek ; _ => - mkV leka (lek + "er") lek (lek +"te") (lek +"t") (lek +"t") + mk6V leka (lek + "er") lek (lek +"te") (lek +"t") (lek +"t") } } ; conj3 : Str -> V = \bo -> - mkV bo (bo + "r") bo (bo +"dde") (bo +"tt") (bo +"dd") ; + mk6V bo (bo + "r") bo (bo +"dde") (bo +"tt") (bo +"dd") ; irregV = \sälja, sålde, sålt -> let @@ -486,18 +525,37 @@ oper _ => init sålt + "d" } in - mkV sälja (säljer.s ! VF (VPres Act)) (säljer.s ! (VF (VImper Act))) sålde sålt såld + mk6V sälja (säljer.s ! VF (VPres Act)) (säljer.s ! (VF (VImper Act))) sålde sålt såld ** {s1 = [] ; lock_V = <>} ; partV v p = {s = v.s ; part = p ; vtype = v.vtype ; lock_V = <>} ; depV v = {s = v.s ; part = v.part ; vtype = VPass ; lock_V = <>} ; reflV v = {s = v.s ; part = v.part ; vtype = VRefl ; lock_V = <>} ; - mkV2 v p = v ** {c2 = p.s ; lock_V2 = <>} ; - dirV2 v = mkV2 v noPrep ; + mkV2 = overload { + mkV2 : (läser : Str) -> V2 = \v -> dirV2 (regV v) ; + mkV2 : V -> V2 = dirV2 ; + mkV2 : V -> Prep -> V2 = mmkV2 + } ; - mkV3 v p q = v ** {c2 = p.s ; c3 = q.s ; lock_V3 = <>} ; - dirV3 v p = mkV3 v noPrep p ; + + mmkV2 v p = v ** {c2 = p.s ; lock_V2 = <>} ; + dirV2 v = mmkV2 v noPrep ; + + mkV3 = overload { + mkV3 : Str -> V3 = \v -> dirdirV3 (regV v) ; + mkV3 : V -> V3 = dirdirV3 ; + mkV3 : V -> Prep -> V3 = dirV3 ; + mkV3 : V -> Prep -> Prep -> V3 = mmkV3 + } ; + + mmkV3 : V -> Prep -> Prep -> V3 ; -- tala, med, om + dirV3 : V -> Prep -> V3 ; -- ge, (acc),till + dirdirV3 : V -> V3 ; -- ge, (dat), (acc) + + + mmkV3 v p q = v ** {c2 = p.s ; c3 = q.s ; lock_V3 = <>} ; + dirV3 v p = mmkV3 v noPrep p ; dirdirV3 v = dirV3 v noPrep ; mkV0 v = v ** {lock_V0 = <>} ; @@ -506,20 +564,52 @@ oper mkVQ v = v ** {lock_VQ = <>} ; mkVA v = v ** {lock_VA = <>} ; - mkV2A v p = mkV2 v p ** {lock_V2A = <>} ; + mkV2A v p = mmkV2 v p ** {lock_V2A = <>} ; V0 : Type = V ; V2S, V2V, V2Q, V2A : Type = V2 ; AS, A2S, AV : Type = A ; A2V : Type = A2 ; - mkV2S v p = mkV2 v p ** {lock_V2 = <>} ; - mkV2V v p t = mkV2 v p ** {s3 = t ; lock_V2 = <>} ; - mkV2Q v p = mkV2 v p ** {lock_V2 = <>} ; + mkV2S v p = mmkV2 v p ** {lock_V2 = <>} ; + mkV2V v p t = mmkV2 v p ** {s3 = t ; lock_V2 = <>} ; + mkV2Q v p = mmkV2 v p ** {lock_V2 = <>} ; mkAS v = v ** {lock_A = <>} ; mkA2S v p = mkA2 v p ** {lock_A = <>} ; mkAV v = v ** {lock_A = <>} ; mkA2V v p = mkA2 v p ** {lock_A = <>} ; +----------Obsolete + +-- To form a noun phrase that can also be plural and have an irregular +-- genitive, you can use the worst-case function. + + mkNP : Str -> Str -> Number -> Gender -> NP ; + + + + regGenPN : Str -> Gender -> PN ; + regPN : Str -> PN ; -- utrum + +-- Sometimes you can reuse a common noun as a proper name, e.g. "Bank". + + nounPN : N -> PN ; + +-- Sometimes just the positive forms are irregular. + + mk3A : (galen,galet,galna : Str) -> A ; + + mk6V : (supa,super,sup,söp,supit,supen : Str) -> V ; + regV : (talar : Str) -> V ; + mk2V : (leka,lekte : Str) -> V ; + irregV : (dricka, drack, druckit : Str) -> V ; + + partV : V -> Str -> V ; + + mmkV2 : V -> Prep -> V2 ; + + dirV2 : V -> V2 ; + + } ;